Question

Solve the equation $2x^2+x+1=0$

Answer 1

Step $1:$ Given $2x^2+x+1=0$

Step 2: Check nature of roots
$D=b^2-4ac$
$a=2,b=1,c=1$
$\Rightarrow D=1-8=-7<0$
$\therefore D$ is Negative.
$\therefore$ Roots are imaginary, so we can use the quadratic formula.

Step 3: Using quadratic formula.
$x=\frac{-b\pm \sqrt{(b^2-4ac}}{2a}$
By putting the values of $a,b,c$
$x=\frac{-1\pm \sqrt{1-8}}{4}$
$\Rightarrow x=\frac{-1\pm \sqrt{-7}}{4}\Rightarrow x=\frac{-1\pm \sqrt{-7}i}{4}$ $\because \sqrt{-1}=i$

The values of $x$ are $\frac{-1+\sqrt{7}i}{4},\frac{-1-\sqrt{7}i}{4}$